The decree authorises the state to "adopt all necessary emergency measures to ration essential public services in order for the Rio 2016 Olympic Games and Paralympic Games to take place."
"Any institutional instability would hurt the country's image," said the decree, signed by acting governor Francisco Dornelles.
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The events pose "serious difficulties in delivering essential public services and could even cause a collapse in public safety, health, education, transportation and environmental management," the decree said.
Rio de Janeiro state is in financial straits due to the fall in global oil prices, while Brazil overall is floundering through a deep recession.
Police, teachers and other government workers in Rio state have seen paychecks delayed because of the cash crunch. Retirees have protested because of unpaid pensions.
Brazil's economy shrank 3.8% last year, its worst recession in 25 years. The International Monetary Fund and the market are predicting a similar contraction this year.
Amnesty International expressed concern at the cuts to social services, which could affect the training of security agents to work in the crime-ridden slums known as favelas.
The decision to cut services and security ahead of the Olympic Games "is not only a shock but is also incredibly worrying, especially given the bad history of police killings and murders," Amnesty's Brazil director, Atila Roque, said in a statement.
Rio's state budget shows a $5.6 billion shortfall for 2016. Royalties from oil -- the state's main revenue-earner -- are projected to collapse from $3.5 billion in 2014 to just $1 billion this year.
Dornelles has called the situation in his state "tragic."
He urged the national government to step up, and pressed authorities to look at what public assets could be sold off to raise cash.
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